Research On Dynamic Characteristics And Vibration Control Of Flexible Manipulator

In the automated production industry,flexible robotic arms are widely used in many fields such as space detection,automated manufacturing,construction,mining,and hazardous operations because of their light weight and low energy consumption.However,the elastic vibration problem of the flexible robotic manipulator affects its speed of movement and positioning accuracy,and reduces the quality and efficiency of industrial production.The vibration problem becomes the main obstacle to the high-speed and high-precision objectives of flexible manipulators.Therefore,how to restrain the vibration of the flexible arm during the movement is an urgent problem to be solved.In this paper,the flexible manipulator is considered as a Euler-Bernoulli beam according to its physical characteristics.The bending vibration equation of the flexible manipulator is obtained by using the mechanics related knowledge,and the vibration mode function and natural frequency are calculated.The dynamic mathematics model of the whole system of the flexible manipulator is established using Lagrange equation,and it is transformed into the state-space equation.The truncation method simplifies the state equation of the motion system space and the accuracy of the modal truncation method is verified by Simulink.Secondly,the linear quadratic optimal control method is applied to the flexible arm vibration damping strategy to establish the corresponding objective function.In order to explore the influence of the value of each element in the weighted matrix on the control effect,a number of groups of data are set up to carry out numerical simulation,and the influence laws of the coefficients are summarized according to the simulation results;the appropriate value is selected as the weighted matrix,the linear optimal control is applied to control the vibration of the manipulator,and its effectiveness is verified by simulation.Then,the distributed parameter boundary control method is applied to suppress the vibration of the manipulator.On the basis of the Lagrange dynamics equation of the manipulator system,the Hamilton method is used to list the specific partial differential equations,and the Lyapunov function is designed according to the control requirements and then the relative control rate is constructed.The flexible arm under the joint torque control is compared with the flexible arm controlled by the joint torque and the end boundary,thedynamic responses of two kinds of control verify the effectiveness of terminal boundary input for vibration control of flexible manipulator.Finally,passive vibration control of mechanical arm is carried out by adding shock absorber on the manipulator.The dynamic equations of the system in the collision process of the linear damping damper and the manipulator are obtained by theoretical calculation and mathematical deduction.The accuracy of the numerical calculation process and the damping effect of the damper are verified by the simple experiment.The nonlinear vibration absorber is tested by observing the energy stored in the shock absorber when the main body vibrates.The effect of vibration is simulated,and the energy absorption values of the system response and the nonlinear damper are simulated,and the damping effect is explained.